Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces. (May 2020)

• Record Type: Journal Article
• Authors: Bulíček, Miroslav; Gwiazda, Piotr; Kalousek, Martin; Świerczewska-Gwiazda, Agnieszka
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 35B27 -- 35J47 -- 76M50; Nonlinear elliptic problem -- Existence of solution -- Homogenization -- Musielak–Orlicz spaces -- Fast growth; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.03.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a strongly nonlinear elliptic problem with the homogeneous Dirichlet boundary condition. The growth and the coercivity of the elliptic operator is assumed to be indicated by an inhomogeneous anisotropic N -function. First, an existence result is shown under the assumption that the N -function or its convex conjugate satisfies Δ 2 -condition. The second result concerns the homogenization process for families of strongly nonlinear elliptic problems with the homogeneous Dirichlet boundary condition under above stated conditions on the elliptic operator, which is additionally assumed to be periodic in the spatial variable.